A note on simple $K3$ singularities and families of weighted $K3$ surfaces

Makiko Mase

A note on simple $K3$ singularities and families of weighted $K3$ surfaces

Algebraic Geometry 2023-05-09 v1

Authors: Makiko Mase

Abstract

We discuss properties of the Seifert form for simple $K3$ singularities, and of the Picard lattices of families of weighted $K3$ surfaces. We study a collection $\mathcal{M}_{(\rho,\,\delta)}$ of $K3$ surfaces polarized by their Picard lattices that are in the set $\mathcal{L}_{(\rho,\,\delta)}$ of certain lattices. We also report a numerical formula that relates the Seifert form for the singularities and the Picard lattice of the family.

Keywords

simple k3 singularities seifert form weighted k3 surfaces picard lattice polarized k3 surfaces numerical formula

Cite

@article{arxiv.2305.04418,
  title  = {A note on simple $K3$ singularities and families of weighted $K3$ surfaces},
  author = {Makiko Mase},
  journal= {arXiv preprint arXiv:2305.04418},
  year   = {2023}
}

Comments

35 pages, 10 tables, 1 figure. To appear in Rendiconti del Circolo Matematico di Palermo Series 2

A note on simple $K3$ singularities and families of weighted $K3$ surfaces

Abstract

Keywords

Cite

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